Hi Evelina
I agree with the suggestion to contact the Archive at Worcester first,
The Worcs Archive does hold the Archive of the West Mercia Police which would cover Malvern, The records seem to be still at the cataloguing stage and the period you want may be subject to legal closure.
Read this:-
http://www.worcestershire.gov.uk/news/article/100/historical_police_records_to_be_displayedDated Dec 2014 of it states:
"Worcestershire Archives and Archaeology Service, based at The Hive, has been awarded funding to help bring historical police records onto public display.
Police archives will be available for the public to view at The Hive after being awarded £42,000 to catalogue and make available the West Mercia Police archives as part of the National Cataloguing Grant programme, administered by The National Archives and funded by The Pilgrim Trust.
Criminal Records of the Marches, as the project is called, will be fully catalogued over the next 15 months for them to be made available to the public."
and then try a search here:-
http://e-services.worcestershire.gov.uk/CalmView/As regards Birmingham, I guess, but don't know, that Birmingham was probably part of the Warwickshire Constabulary. Their records are held at the Warwickshire Archive.
The following is taken from the Warwickshire Heritage and Culture website:-
“The records of the Warwickshire Constabulary dating from 1840 have been deposited: they contain much information about the administration of the police service and the careers of individual police officers, but very little about criminals”
It's worth an email to Warwickshire Archive to check that Birmingham was part of the Warwickshire Constabulary in the period you are referrring to.
Jack